City, the 2023 Champions League winners, will host Madrid at Etihad Stadium on 11 or 12 February before travelling to Spain for the second leg the following week.
Celtic, the first British club to win the trophy when they did so in 1967, will face Bayern Munich at Celtic Park before the Bundesliga club host Brendan Rodgers’ side at Allianz Arena in the second leg.
The winners of City’s tie against Madrid and Celtic’s meeting with Bayern will face either German side Bayer Leverkusen or Spanish club Atletico Madrid in the last 16.
The draw for the last 16 is on 21 February, following the conclusion of the play-off ties, but some elements of that draw are pre-determined.
Champions League play-off draw in full
Brest v Paris St-Germain
Club Brugge v Atalanta
Manchester City v Real Madrid
Juventus v PSV Eindhoven
Monaco v Benfica
Sporting v Borussia Dortmund
Celtic v Bayern Munich
Feyenoord v AC Milan
Clubs that finished in the top eight of the 36-team Champions League group table progressed directly to the last 16.
The teams in the bottom eight were eliminated.
The remaining 16 teams that finished between ninth and 24th place progressed into the play-offs.
Of those 16 teams, the clubs that finished ninth to 16th in the league phase were seeded into four pairs for the play-off draw.
Those that finished from 17th to 24th were put into four unseeded pairs.
Unseeded teams were drawn against one of two seeded teams, with seeded teams hosting the second leg of the play-off as they finished higher in the first phase table.
City finished 22nd in the league table while Celtic finished 21st.
It meant the two sides would face one of Real Madrid or Bayern Munich, who finished 11th and 12th respectively in the group stage.
Liverpool, Arsenal and Aston Villa progressed straight to the last 16 after finishing in the top eight of the league phase.
The draw to finalise the last-16 ties is made on 21 February, when the eight winners of the play-off ties will be known.
Some elements of the last-16 draw are already decided because teams in the top eight of the league phase were split into four seeded pairs based on their position in the table.
Teams in the seeded pair will face the winners of one of the two play-off ties they have already been bracketed with.
Liverpool finished top of the league phase and are paired with second-place Barcelona.
Those teams will play either the winners of the Brest v Paris St-Germain tie or the team that progresses from Monaco’s meeting with Benfica.
Arsenal were third and are paired with Italian club Inter Milan, who were fourth.
The Gunners or Inter will play either the winners of Juventus v PSV Eindhoven or Feyenoord against AC Milan.
Villa were eighth and are paired with seventh-placed Lille and those teams will face the winners of Club Brugge v Atalanta or Sporting v Borussia Dortmund.
In the Europa League, which follows the same format as the Champions League, AZ Alkmaar face Galatasaray and Midtjylland will play Real Sociedad in the play-offs.
The winners of those ties will face either Manchester United or Tottenham Hotspur in the last 16.
Twente will play Bodo/Glimt and Jose Mourinho’s Fenerbahce have been drawn against Anderlecht, with one of the winners of those two ties then facing Rangers.
United and Spurs were third and fourth in the 36-team Europa League group stage respectively, and with Rangers finishing eighth it meant all three British sides qualified automatically for the last 16.
Notable ties include two-time winners Porto playing 1984 European Cup finalists Roma, while Hungarian side Ferencvaros – managed by former Tottenham striker Robbie Keane – play Viktoria Plzen.
The winners of those two ties will be drawn against either Lazio or Athletic Bilbao.
As with the Champions League, the last-16 draw will be made on 21 February once the eight winners of the play-off ties are known.
That will complete the brackets and teams will know their routes to the final.
The two-legged play-off ties are on 13 and 20 February, with the last-16 matches scheduled for 6 and 13 March.
Europa League play-off draw in full
Ferencvaros v Viktoria Plzen
Porto v Roma
AZ Alkmaar v Galatasaray
Midtjylland v Real Sociedad
Union Saint-Gilloise v Ajax
PAOK v FCSB
Twente v Bodo/Glimt
Fenerbahce v Anderlecht
